Question

prove that :-sin2θ+cos4θ=cos2θ+sin4θ​

Answer 1

Answer:

$sin^2\theta+cos^4\theta =cos^2\theta+sin^4\theta$

Step-by-step explanation:

LHS $= sin^2\theta+cos^4\theta$

$= sin^2\theta+(cos^2\theta)^2$----- (1)

We know that $sin^ \theta + cos^2\theta = 1$

So, $cos^2\theta = 1- sin^2\theta$ Put in (1)

$= sin^2\theta+(1- sin^2\theta)^2$

$= sin^2\theta + 1 - 2 sin^2\theta + sin^4\theta$

$= 1 + sin^2\theta - 2 sin^2\theta + sin^4\theta$

$= 1 - sin^2\theta + sin^4\theta$

$=cos^2\theta+sin^4\theta$

= RHS

So, $sin^2\theta+cos^4\theta =cos^2\theta+sin^4\theta$